Numerical solution of a generalized elliptic partial differential eigenvalue problem

In this article we discuss a method for the solution of non-separable eigen value problems. These problems are taken to be elliptic and linear and aris e in a whole host of physically interesting problems. The approach exploits finite differences and a pseudo-spectral scheme. We elect to normalise at a single point, which is usually internal to the domain, and exploit the fa ct that the partial differential equation has not been satisfied at this po int to determine whether we have an eigenvalue of the system. The eigenvalu e solver is of a local nature and is consequently relatively inexpensive to run. (C) Academic Press.